#ifndef _DSP_MATH_SHARED_H_
#define _DSP_MATH_SHARED_H_

#include <math.h>

#pragma warning(disable:4244)

#define PI 3.1415926535897932384626433832795

template<class REAL>
class fft
{
public:
	/*
	Fast Fourier/Cosine/Sine Transform
		dimension   :one
		data length :power of 2
		decimation  :frequency
		radix       :split-radix
		data        :inplace
		table       :use
	functions
		cdft: Complex Discrete Fourier Transform
		rdft: Real Discrete Fourier Transform
		ddct: Discrete Cosine Transform
		ddst: Discrete Sine Transform
		dfct: Cosine Transform of RDFT (Real Symmetric DFT)
		dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
	function prototypes
		void cdft(int, int, REAL *, int *, REAL *);
		void rdft(int, int, REAL *, int *, REAL *);
		void ddct(int, int, REAL *, int *, REAL *);
		void ddst(int, int, REAL *, int *, REAL *);
		void dfct(int, REAL *, REAL *, int *, REAL *);
		void dfst(int, REAL *, REAL *, int *, REAL *);


	-------- Complex DFT (Discrete Fourier Transform) --------
		[definition]
			<case1>
				X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
			<case2>
				X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
			(notes: sum_j=0^n-1 is a summation from j=0 to n-1)
		[usage]
			<case1>
				ip[0] = 0; // first time only
				cdft(2*n, 1, a, ip, w);
			<case2>
				ip[0] = 0; // first time only
				cdft(2*n, -1, a, ip, w);
		[parameters]
			2*n            :data length (int)
							n >= 1, n = power of 2
			a[0...2*n-1]   :input/output data (REAL *)
							input data
								a[2*j] = Re(x[j]),
								a[2*j+1] = Im(x[j]), 0<=j<n
							output data
								a[2*k] = Re(X[k]),
								a[2*k+1] = Im(X[k]), 0<=k<n
			ip[0...*]      :work area for bit reversal (int *)
							length of ip >= 2+sqrt(n)
							strictly,
							length of ip >=
								2+(1<<(int)(log(n+0.5)/log(2))/2).
							ip[0],ip[1] are pointers of the cos/sin table.
			w[0...n/2-1]   :cos/sin table (REAL *)
							w[],ip[] are initialized if ip[0] == 0.
		[remark]
			Inverse of
				cdft(2*n, -1, a, ip, w);
			is
				cdft(2*n, 1, a, ip, w);
				for (j = 0; j <= 2 * n - 1; j++) {
					a[j] *= 1.0 / n;
				}
			.


	-------- Real DFT / Inverse of Real DFT --------
		[definition]
			<case1> RDFT
				R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
				I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
			<case2> IRDFT (excluding scale)
				a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
					   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
					   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
		[usage]
			<case1>
				ip[0] = 0; // first time only
				rdft(n, 1, a, ip, w);
			<case2>
				ip[0] = 0; // first time only
				rdft(n, -1, a, ip, w);
		[parameters]
			n              :data length (int)
							n >= 2, n = power of 2
			a[0...n-1]     :input/output data (REAL *)
							<case1>
								output data
									a[2*k] = R[k], 0<=k<n/2
									a[2*k+1] = I[k], 0<k<n/2
									a[1] = R[n/2]
							<case2>
								input data
									a[2*j] = R[j], 0<=j<n/2
									a[2*j+1] = I[j], 0<j<n/2
									a[1] = R[n/2]
			ip[0...*]      :work area for bit reversal (int *)
							length of ip >= 2+sqrt(n/2)
							strictly,
							length of ip >=
								2+(1<<(int)(log(n/2+0.5)/log(2))/2).
							ip[0],ip[1] are pointers of the cos/sin table.
			w[0...n/2-1]   :cos/sin table (REAL *)
							w[],ip[] are initialized if ip[0] == 0.
		[remark]
			Inverse of
				rdft(n, 1, a, ip, w);
			is
				rdft(n, -1, a, ip, w);
				for (j = 0; j <= n - 1; j++) {
					a[j] *= 2.0 / n;
				}
			.


	-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
		[definition]
			<case1> IDCT (excluding scale)
				C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
			<case2> DCT
				C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
		[usage]
			<case1>
				ip[0] = 0; // first time only
				ddct(n, 1, a, ip, w);
			<case2>
				ip[0] = 0; // first time only
				ddct(n, -1, a, ip, w);
		[parameters]
			n              :data length (int)
							n >= 2, n = power of 2
			a[0...n-1]     :input/output data (REAL *)
							output data
								a[k] = C[k], 0<=k<n
			ip[0...*]      :work area for bit reversal (int *)
							length of ip >= 2+sqrt(n/2)
							strictly,
							length of ip >=
								2+(1<<(int)(log(n/2+0.5)/log(2))/2).
							ip[0],ip[1] are pointers of the cos/sin table.
			w[0...n*5/4-1] :cos/sin table (REAL *)
							w[],ip[] are initialized if ip[0] == 0.
		[remark]
			Inverse of
				ddct(n, -1, a, ip, w);
			is
				a[0] *= 0.5;
				ddct(n, 1, a, ip, w);
				for (j = 0; j <= n - 1; j++) {
					a[j] *= 2.0 / n;
				}
			.


	-------- DST (Discrete Sine Transform) / Inverse of DST --------
		[definition]
			<case1> IDST (excluding scale)
				S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
			<case2> DST
				S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
		[usage]
			<case1>
				ip[0] = 0; // first time only
				ddst(n, 1, a, ip, w);
			<case2>
				ip[0] = 0; // first time only
				ddst(n, -1, a, ip, w);
		[parameters]
			n              :data length (int)
							n >= 2, n = power of 2
			a[0...n-1]     :input/output data (REAL *)
							<case1>
								input data
									a[j] = A[j], 0<j<n
									a[0] = A[n]
								output data
									a[k] = S[k], 0<=k<n
							<case2>
								output data
									a[k] = S[k], 0<k<n
									a[0] = S[n]
			ip[0...*]      :work area for bit reversal (int *)
							length of ip >= 2+sqrt(n/2)
							strictly,
							length of ip >=
								2+(1<<(int)(log(n/2+0.5)/log(2))/2).
							ip[0],ip[1] are pointers of the cos/sin table.
			w[0...n*5/4-1] :cos/sin table (REAL *)
							w[],ip[] are initialized if ip[0] == 0.
		[remark]
			Inverse of
				ddst(n, -1, a, ip, w);
			is
				a[0] *= 0.5;
				ddst(n, 1, a, ip, w);
				for (j = 0; j <= n - 1; j++) {
					a[j] *= 2.0 / n;
				}
			.


	-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
		[definition]
			C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
		[usage]
			ip[0] = 0; // first time only
			dfct(n, a, t, ip, w);
		[parameters]
			n              :data length - 1 (int)
							n >= 2, n = power of 2
			a[0...n]       :input/output data (REAL *)
							output data
								a[k] = C[k], 0<=k<=n
			t[0...n/2]     :work area (REAL *)
			ip[0...*]      :work area for bit reversal (int *)
							length of ip >= 2+sqrt(n/4)
							strictly,
							length of ip >=
								2+(1<<(int)(log(n/4+0.5)/log(2))/2).
							ip[0],ip[1] are pointers of the cos/sin table.
			w[0...n*5/8-1] :cos/sin table (REAL *)
							w[],ip[] are initialized if ip[0] == 0.
		[remark]
			Inverse of
				a[0] *= 0.5;
				a[n] *= 0.5;
				dfct(n, a, t, ip, w);
			is
				a[0] *= 0.5;
				a[n] *= 0.5;
				dfct(n, a, t, ip, w);
				for (j = 0; j <= n; j++) {
					a[j] *= 2.0 / n;
				}
			.


	-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
		[definition]
			S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
		[usage]
			ip[0] = 0; // first time only
			dfst(n, a, t, ip, w);
		[parameters]
			n              :data length + 1 (int)
							n >= 2, n = power of 2
			a[0...n-1]     :input/output data (REAL *)
							output data
								a[k] = S[k], 0<k<n
							(a[0] is used for work area)
			t[0...n/2-1]   :work area (REAL *)
			ip[0...*]      :work area for bit reversal (int *)
							length of ip >= 2+sqrt(n/4)
							strictly,
							length of ip >=
								2+(1<<(int)(log(n/4+0.5)/log(2))/2).
							ip[0],ip[1] are pointers of the cos/sin table.
			w[0...n*5/8-1] :cos/sin table (REAL *)
							w[],ip[] are initialized if ip[0] == 0.
		[remark]
			Inverse of
				dfst(n, a, t, ip, w);
			is
				dfst(n, a, t, ip, w);
				for (j = 1; j <= n - 1; j++) {
					a[j] *= 2.0 / n;
				}
			.


	Appendix :
		The cos/sin table is recalculated when the larger table required.
		w[] and ip[] are compatible with all routines.
	*/


	static void cdft(int n, int isgn, REAL *a, int *ip, REAL *w)
	{
		int nw;

		nw = ip[0];
		if (n > (nw << 2)) {
			nw = n >> 2;
			makewt(nw, ip, w);
		}
		if (isgn >= 0) {
			cftfsub(n, a, ip + 2, nw, w);
		} else {
			cftbsub(n, a, ip + 2, nw, w);
		}
	}


	static void rdft(int n, int isgn, REAL *a, int *ip, REAL *w)
	{
		int nw, nc;
		REAL xi;

		nw = ip[0];
		if (n > (nw << 2)) {
			nw = n >> 2;
			makewt(nw, ip, w);
		}
		nc = ip[1];
		if (n > (nc << 2)) {
			nc = n >> 2;
			makect(nc, ip, w + nw);
		}
		if (isgn >= 0) {
			if (n > 4) {
				cftfsub(n, a, ip + 2, nw, w);
				rftfsub(n, a, nc, w + nw);
			} else if (n == 4) {
				cftfsub(n, a, ip + 2, nw, w);
			}
			xi = a[0] - a[1];
			a[0] += a[1];
			a[1] = xi;
		} else {
			a[1] = 0.5 * (a[0] - a[1]);
			a[0] -= a[1];
			if (n > 4) {
				rftbsub(n, a, nc, w + nw);
				cftbsub(n, a, ip + 2, nw, w);
			} else if (n == 4) {
				cftbsub(n, a, ip + 2, nw, w);
			}
		}
	}


	static void ddct(int n, int isgn, REAL *a, int *ip, REAL *w)
	{
		int j, nw, nc;
		REAL xr;

		nw = ip[0];
		if (n > (nw << 2)) {
			nw = n >> 2;
			makewt(nw, ip, w);
		}
		nc = ip[1];
		if (n > nc) {
			nc = n;
			makect(nc, ip, w + nw);
		}
		if (isgn < 0) {
			xr = a[n - 1];
			for (j = n - 2; j >= 2; j -= 2) {
				a[j + 1] = a[j] - a[j - 1];
				a[j] += a[j - 1];
			}
			a[1] = a[0] - xr;
			a[0] += xr;
			if (n > 4) {
				rftbsub(n, a, nc, w + nw);
				cftbsub(n, a, ip + 2, nw, w);
			} else if (n == 4) {
				cftbsub(n, a, ip + 2, nw, w);
			}
		}
		dctsub(n, a, nc, w + nw);
		if (isgn >= 0) {
			if (n > 4) {
				cftfsub(n, a, ip + 2, nw, w);
				rftfsub(n, a, nc, w + nw);
			} else if (n == 4) {
				cftfsub(n, a, ip + 2, nw, w);
			}
			xr = a[0] - a[1];
			a[0] += a[1];
			for (j = 2; j < n; j += 2) {
				a[j - 1] = a[j] - a[j + 1];
				a[j] += a[j + 1];
			}
			a[n - 1] = xr;
		}
	}


	static void ddst(int n, int isgn, REAL *a, int *ip, REAL *w)
	{
		int j, nw, nc;
		REAL xr;

		nw = ip[0];
		if (n > (nw << 2)) {
			nw = n >> 2;
			makewt(nw, ip, w);
		}
		nc = ip[1];
		if (n > nc) {
			nc = n;
			makect(nc, ip, w + nw);
		}
		if (isgn < 0) {
			xr = a[n - 1];
			for (j = n - 2; j >= 2; j -= 2) {
				a[j + 1] = -a[j] - a[j - 1];
				a[j] -= a[j - 1];
			}
			a[1] = a[0] + xr;
			a[0] -= xr;
			if (n > 4) {
				rftbsub(n, a, nc, w + nw);
				cftbsub(n, a, ip + 2, nw, w);
			} else if (n == 4) {
				cftbsub(n, a, ip + 2, nw, w);
			}
		}
		dstsub(n, a, nc, w + nw);
		if (isgn >= 0) {
			if (n > 4) {
				cftfsub(n, a, ip + 2, nw, w);
				rftfsub(n, a, nc, w + nw);
			} else if (n == 4) {
				cftfsub(n, a, ip + 2, nw, w);
			}
			xr = a[0] - a[1];
			a[0] += a[1];
			for (j = 2; j < n; j += 2) {
				a[j - 1] = -a[j] - a[j + 1];
				a[j] -= a[j + 1];
			}
			a[n - 1] = -xr;
		}
	}


	static void dfct(int n, REAL *a, REAL *t, int *ip, REAL *w)
	{
		int j, k, l, m, mh, nw, nc;
		REAL xr, xi, yr, yi;

		nw = ip[0];
		if (n > (nw << 3)) {
			nw = n >> 3;
			makewt(nw, ip, w);
		}
		nc = ip[1];
		if (n > (nc << 1)) {
			nc = n >> 1;
			makect(nc, ip, w + nw);
		}
		m = n >> 1;
		yi = a[m];
		xi = a[0] + a[n];
		a[0] -= a[n];
		t[0] = xi - yi;
		t[m] = xi + yi;
		if (n > 2) {
			mh = m >> 1;
			for (j = 1; j < mh; j++) {
				k = m - j;
				xr = a[j] - a[n - j];
				xi = a[j] + a[n - j];
				yr = a[k] - a[n - k];
				yi = a[k] + a[n - k];
				a[j] = xr;
				a[k] = yr;
				t[j] = xi - yi;
				t[k] = xi + yi;
			}
			t[mh] = a[mh] + a[n - mh];
			a[mh] -= a[n - mh];
			dctsub(m, a, nc, w + nw);
			if (m > 4) {
				cftfsub(m, a, ip + 2, nw, w);
				rftfsub(m, a, nc, w + nw);
			} else if (m == 4) {
				cftfsub(m, a, ip + 2, nw, w);
			}
			a[n - 1] = a[0] - a[1];
			a[1] = a[0] + a[1];
			for (j = m - 2; j >= 2; j -= 2) {
				a[2 * j + 1] = a[j] + a[j + 1];
				a[2 * j - 1] = a[j] - a[j + 1];
			}
			l = 2;
			m = mh;
			while (m >= 2) {
				dctsub(m, t, nc, w + nw);
				if (m > 4) {
					cftfsub(m, t, ip + 2, nw, w);
					rftfsub(m, t, nc, w + nw);
				} else if (m == 4) {
					cftfsub(m, t, ip + 2, nw, w);
				}
				a[n - l] = t[0] - t[1];
				a[l] = t[0] + t[1];
				k = 0;
				for (j = 2; j < m; j += 2) {
					k += l << 2;
					a[k - l] = t[j] - t[j + 1];
					a[k + l] = t[j] + t[j + 1];
				}
				l <<= 1;
				mh = m >> 1;
				for (j = 0; j < mh; j++) {
					k = m - j;
					t[j] = t[m + k] - t[m + j];
					t[k] = t[m + k] + t[m + j];
				}
				t[mh] = t[m + mh];
				m = mh;
			}
			a[l] = t[0];
			a[n] = t[2] - t[1];
			a[0] = t[2] + t[1];
		} else {
			a[1] = a[0];
			a[2] = t[0];
			a[0] = t[1];
		}
	}


	static void dfst(int n, REAL *a, REAL *t, int *ip, REAL *w)
	{
		int j, k, l, m, mh, nw, nc;
		REAL xr, xi, yr, yi;

		nw = ip[0];
		if (n > (nw << 3)) {
			nw = n >> 3;
			makewt(nw, ip, w);
		}
		nc = ip[1];
		if (n > (nc << 1)) {
			nc = n >> 1;
			makect(nc, ip, w + nw);
		}
		if (n > 2) {
			m = n >> 1;
			mh = m >> 1;
			for (j = 1; j < mh; j++) {
				k = m - j;
				xr = a[j] + a[n - j];
				xi = a[j] - a[n - j];
				yr = a[k] + a[n - k];
				yi = a[k] - a[n - k];
				a[j] = xr;
				a[k] = yr;
				t[j] = xi + yi;
				t[k] = xi - yi;
			}
			t[0] = a[mh] - a[n - mh];
			a[mh] += a[n - mh];
			a[0] = a[m];
			dstsub(m, a, nc, w + nw);
			if (m > 4) {
				cftfsub(m, a, ip + 2, nw, w);
				rftfsub(m, a, nc, w + nw);
			} else if (m == 4) {
				cftfsub(m, a, ip + 2, nw, w);
			}
			a[n - 1] = a[1] - a[0];
			a[1] = a[0] + a[1];
			for (j = m - 2; j >= 2; j -= 2) {
				a[2 * j + 1] = a[j] - a[j + 1];
				a[2 * j - 1] = -a[j] - a[j + 1];
			}
			l = 2;
			m = mh;
			while (m >= 2) {
				dstsub(m, t, nc, w + nw);
				if (m > 4) {
					cftfsub(m, t, ip + 2, nw, w);
					rftfsub(m, t, nc, w + nw);
				} else if (m == 4) {
					cftfsub(m, t, ip + 2, nw, w);
				}
				a[n - l] = t[1] - t[0];
				a[l] = t[0] + t[1];
				k = 0;
				for (j = 2; j < m; j += 2) {
					k += l << 2;
					a[k - l] = -t[j] - t[j + 1];
					a[k + l] = t[j] - t[j + 1];
				}
				l <<= 1;
				mh = m >> 1;
				for (j = 1; j < mh; j++) {
					k = m - j;
					t[j] = t[m + k] + t[m + j];
					t[k] = t[m + k] - t[m + j];
				}
				t[0] = t[m + mh];
				m = mh;
			}
			a[l] = t[0];
		}
		a[0] = 0;
	}



	static void makewt(int nw, int *ip, REAL *w)
	{
		int j, nwh, nw0, nw1;
		REAL delta, wn4r, wk1r, wk1i, wk3r, wk3i;

		ip[0] = nw;
		ip[1] = 1;
		if (nw > 2) {
			nwh = nw >> 1;
			delta = atan(1.0) / nwh;
			wn4r = cos(delta * nwh);
			w[0] = 1;
			w[1] = wn4r;
			if (nwh >= 4) {
				w[2] = 0.5 / cos(delta * 2);
				w[3] = 0.5 / cos(delta * 6);
			}
			for (j = 4; j < nwh; j += 4) {
				w[j] = cos(delta * j);
				w[j + 1] = sin(delta * j);
				w[j + 2] = cos(3 * delta * j);
				w[j + 3] = sin(3 * delta * j);
			}
			nw0 = 0;
			while (nwh > 2) {
				nw1 = nw0 + nwh;
				nwh >>= 1;
				w[nw1] = 1;
				w[nw1 + 1] = wn4r;
				if (nwh >= 4) {
					wk1r = w[nw0 + 4];
					wk3r = w[nw0 + 6];
					w[nw1 + 2] = 0.5 / wk1r;
					w[nw1 + 3] = 0.5 / wk3r;
				}
				for (j = 4; j < nwh; j += 4) {
					wk1r = w[nw0 + 2 * j];
					wk1i = w[nw0 + 2 * j + 1];
					wk3r = w[nw0 + 2 * j + 2];
					wk3i = w[nw0 + 2 * j + 3];
					w[nw1 + j] = wk1r;
					w[nw1 + j + 1] = wk1i;
					w[nw1 + j + 2] = wk3r;
					w[nw1 + j + 3] = wk3i;
				}
				nw0 = nw1;
			}
		}
	}


	static void makect(int nc, int *ip, REAL *c)
	{
		int j, nch;
		REAL delta;

		ip[1] = nc;
		if (nc > 1) {
			nch = nc >> 1;
			delta = atan(1.0) / nch;
			c[0] = cos(delta * nch);
			c[nch] = 0.5 * c[0];
			for (j = 1; j < nch; j++) {
				c[j] = 0.5 * cos(delta * j);
				c[nc - j] = 0.5 * sin(delta * j);
			}
		}
	}


	/* -------- child routines -------- */


	#ifndef CDFT_RECURSIVE_N  /* length of the recursive FFT mode */
	#define CDFT_RECURSIVE_N 512  /* <= (L1 cache size) / 16 */
	#endif


	static void cftfsub(int n, REAL *a, int *ip, int nw, REAL *w)
	{
		int m;

		if (n > 32) {
			m = n >> 2;
			cftf1st(n, a, &w[nw - m]);
			if (n > CDFT_RECURSIVE_N) {
				cftrec1(m, a, nw, w);
				cftrec2(m, &a[m], nw, w);
				cftrec1(m, &a[2 * m], nw, w);
				cftrec1(m, &a[3 * m], nw, w);
			} else if (m > 32) {
				cftexp1(n, a, nw, w);
			} else {
				cftfx41(n, a, nw, w);
			}
			bitrv2(n, ip, a);
		} else if (n > 8) {
			if (n == 32) {
				cftf161(a, &w[nw - 8]);
				bitrv216(a);
			} else {
				cftf081(a, w);
				bitrv208(a);
			}
		} else if (n == 8) {
			cftf040(a);
		} else if (n == 4) {
			cftx020(a);
		}
	}


	static void cftbsub(int n, REAL *a, int *ip, int nw, REAL *w)
	{
		int m;

		if (n > 32) {
			m = n >> 2;
			cftb1st(n, a, &w[nw - m]);
			if (n > CDFT_RECURSIVE_N) {
				cftrec1(m, a, nw, w);
				cftrec2(m, &a[m], nw, w);
				cftrec1(m, &a[2 * m], nw, w);
				cftrec1(m, &a[3 * m], nw, w);
			} else if (m > 32) {
				cftexp1(n, a, nw, w);
			} else {
				cftfx41(n, a, nw, w);
			}
			bitrv2conj(n, ip, a);
		} else if (n > 8) {
			if (n == 32) {
				cftf161(a, &w[nw - 8]);
				bitrv216neg(a);
			} else {
				cftf081(a, w);
				bitrv208neg(a);
			}
		} else if (n == 8) {
			cftb040(a);
		} else if (n == 4) {
			cftx020(a);
		}
	}


	static void bitrv2(int n, int *ip, REAL *a)
	{
		int j, j1, k, k1, l, m, m2;
		REAL xr, xi, yr, yi;

		ip[0] = 0;
		l = n;
		m = 1;
		while ((m << 3) < l) {
			l >>= 1;
			for (j = 0; j < m; j++) {
				ip[m + j] = ip[j] + l;
			}
			m <<= 1;
		}
		m2 = 2 * m;
		if ((m << 3) == l) {
			for (k = 0; k < m; k++) {
				for (j = 0; j < k; j++) {
					j1 = 2 * j + ip[k];
					k1 = 2 * k + ip[j];
					xr = a[j1];
					xi = a[j1 + 1];
					yr = a[k1];
					yi = a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 += 2 * m2;
					xr = a[j1];
					xi = a[j1 + 1];
					yr = a[k1];
					yi = a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 -= m2;
					xr = a[j1];
					xi = a[j1 + 1];
					yr = a[k1];
					yi = a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 += 2 * m2;
					xr = a[j1];
					xi = a[j1 + 1];
					yr = a[k1];
					yi = a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
				}
				j1 = 2 * k + m2 + ip[k];
				k1 = j1 + m2;
				xr = a[j1];
				xi = a[j1 + 1];
				yr = a[k1];
				yi = a[k1 + 1];
				a[j1] = yr;
				a[j1 + 1] = yi;
				a[k1] = xr;
				a[k1 + 1] = xi;
			}
		} else {
			for (k = 1; k < m; k++) {
				for (j = 0; j < k; j++) {
					j1 = 2 * j + ip[k];
					k1 = 2 * k + ip[j];
					xr = a[j1];
					xi = a[j1 + 1];
					yr = a[k1];
					yi = a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 += m2;
					xr = a[j1];
					xi = a[j1 + 1];
					yr = a[k1];
					yi = a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
				}
			}
		}
	}


	static void bitrv2conj(int n, int *ip, REAL *a)
	{
		int j, j1, k, k1, l, m, m2;
		REAL xr, xi, yr, yi;

		ip[0] = 0;
		l = n;
		m = 1;
		while ((m << 3) < l) {
			l >>= 1;
			for (j = 0; j < m; j++) {
				ip[m + j] = ip[j] + l;
			}
			m <<= 1;
		}
		m2 = 2 * m;
		if ((m << 3) == l) {
			for (k = 0; k < m; k++) {
				for (j = 0; j < k; j++) {
					j1 = 2 * j + ip[k];
					k1 = 2 * k + ip[j];
					xr = a[j1];
					xi = -a[j1 + 1];
					yr = a[k1];
					yi = -a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 += 2 * m2;
					xr = a[j1];
					xi = -a[j1 + 1];
					yr = a[k1];
					yi = -a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 -= m2;
					xr = a[j1];
					xi = -a[j1 + 1];
					yr = a[k1];
					yi = -a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 += 2 * m2;
					xr = a[j1];
					xi = -a[j1 + 1];
					yr = a[k1];
					yi = -a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
				}
				k1 = 2 * k + ip[k];
				a[k1 + 1] = -a[k1 + 1];
				j1 = k1 + m2;
				k1 = j1 + m2;
				xr = a[j1];
				xi = -a[j1 + 1];
				yr = a[k1];
				yi = -a[k1 + 1];
				a[j1] = yr;
				a[j1 + 1] = yi;
				a[k1] = xr;
				a[k1 + 1] = xi;
				k1 += m2;
				a[k1 + 1] = -a[k1 + 1];
			}
		} else {
			a[1] = -a[1];
			a[m2 + 1] = -a[m2 + 1];
			for (k = 1; k < m; k++) {
				for (j = 0; j < k; j++) {
					j1 = 2 * j + ip[k];
					k1 = 2 * k + ip[j];
					xr = a[j1];
					xi = -a[j1 + 1];
					yr = a[k1];
					yi = -a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
					j1 += m2;
					k1 += m2;
					xr = a[j1];
					xi = -a[j1 + 1];
					yr = a[k1];
					yi = -a[k1 + 1];
					a[j1] = yr;
					a[j1 + 1] = yi;
					a[k1] = xr;
					a[k1 + 1] = xi;
				}
				k1 = 2 * k + ip[k];
				a[k1 + 1] = -a[k1 + 1];
				a[k1 + m2 + 1] = -a[k1 + m2 + 1];
			}
		}
	}


	static void bitrv216(REAL *a)
	{
		REAL x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
			x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i,
			x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;

		x1r = a[2];
		x1i = a[3];
		x2r = a[4];
		x2i = a[5];
		x3r = a[6];
		x3i = a[7];
		x4r = a[8];
		x4i = a[9];
		x5r = a[10];
		x5i = a[11];
		x7r = a[14];
		x7i = a[15];
		x8r = a[16];
		x8i = a[17];
		x10r = a[20];
		x10i = a[21];
		x11r = a[22];
		x11i = a[23];
		x12r = a[24];
		x12i = a[25];
		x13r = a[26];
		x13i = a[27];
		x14r = a[28];
		x14i = a[29];
		a[2] = x8r;
		a[3] = x8i;
		a[4] = x4r;
		a[5] = x4i;
		a[6] = x12r;
		a[7] = x12i;
		a[8] = x2r;
		a[9] = x2i;
		a[10] = x10r;
		a[11] = x10i;
		a[14] = x14r;
		a[15] = x14i;
		a[16] = x1r;
		a[17] = x1i;
		a[20] = x5r;
		a[21] = x5i;
		a[22] = x13r;
		a[23] = x13i;
		a[24] = x3r;
		a[25] = x3i;
		a[26] = x11r;
		a[27] = x11i;
		a[28] = x7r;
		a[29] = x7i;
	}


	static void bitrv216neg(REAL *a)
	{
		REAL x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
			x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i,
			x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i,
			x13r, x13i, x14r, x14i, x15r, x15i;

		x1r = a[2];
		x1i = a[3];
		x2r = a[4];
		x2i = a[5];
		x3r = a[6];
		x3i = a[7];
		x4r = a[8];
		x4i = a[9];
		x5r = a[10];
		x5i = a[11];
		x6r = a[12];
		x6i = a[13];
		x7r = a[14];
		x7i = a[15];
		x8r = a[16];
		x8i = a[17];
		x9r = a[18];
		x9i = a[19];
		x10r = a[20];
		x10i = a[21];
		x11r = a[22];
		x11i = a[23];
		x12r = a[24];
		x12i = a[25];
		x13r = a[26];
		x13i = a[27];
		x14r = a[28];
		x14i = a[29];
		x15r = a[30];
		x15i = a[31];
		a[2] = x15r;
		a[3] = x15i;
		a[4] = x7r;
		a[5] = x7i;
		a[6] = x11r;
		a[7] = x11i;
		a[8] = x3r;
		a[9] = x3i;
		a[10] = x13r;
		a[11] = x13i;
		a[12] = x5r;
		a[13] = x5i;
		a[14] = x9r;
		a[15] = x9i;
		a[16] = x1r;
		a[17] = x1i;
		a[18] = x14r;
		a[19] = x14i;
		a[20] = x6r;
		a[21] = x6i;
		a[22] = x10r;
		a[23] = x10i;
		a[24] = x2r;
		a[25] = x2i;
		a[26] = x12r;
		a[27] = x12i;
		a[28] = x4r;
		a[29] = x4i;
		a[30] = x8r;
		a[31] = x8i;
	}


	static void bitrv208(REAL *a)
	{
		REAL x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;

		x1r = a[2];
		x1i = a[3];
		x3r = a[6];
		x3i = a[7];
		x4r = a[8];
		x4i = a[9];
		x6r = a[12];
		x6i = a[13];
		a[2] = x4r;
		a[3] = x4i;
		a[6] = x6r;
		a[7] = x6i;
		a[8] = x1r;
		a[9] = x1i;
		a[12] = x3r;
		a[13] = x3i;
	}


	static void bitrv208neg(REAL *a)
	{
		REAL x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
			x5r, x5i, x6r, x6i, x7r, x7i;

		x1r = a[2];
		x1i = a[3];
		x2r = a[4];
		x2i = a[5];
		x3r = a[6];
		x3i = a[7];
		x4r = a[8];
		x4i = a[9];
		x5r = a[10];
		x5i = a[11];
		x6r = a[12];
		x6i = a[13];
		x7r = a[14];
		x7i = a[15];
		a[2] = x7r;
		a[3] = x7i;
		a[4] = x3r;
		a[5] = x3i;
		a[6] = x5r;
		a[7] = x5i;
		a[8] = x1r;
		a[9] = x1i;
		a[10] = x6r;
		a[11] = x6i;
		a[12] = x2r;
		a[13] = x2i;
		a[14] = x4r;
		a[15] = x4i;
	}


	static void cftf1st(int n, REAL *a, REAL *w)
	{
		int j, j0, j1, j2, j3, k, m, mh;
		REAL wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
			wd1r, wd1i, wd3r, wd3i;
		REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
			y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;

		mh = n >> 3;
		m = 2 * mh;
		j1 = m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[0] + a[j2];
		x0i = a[1] + a[j2 + 1];
		x1r = a[0] - a[j2];
		x1i = a[1] - a[j2 + 1];
		x2r = a[j1] + a[j3];
		x2i = a[j1 + 1] + a[j3 + 1];
		x3r = a[j1] - a[j3];
		x3i = a[j1 + 1] - a[j3 + 1];
		a[0] = x0r + x2r;
		a[1] = x0i + x2i;
		a[j1] = x0r - x2r;
		a[j1 + 1] = x0i - x2i;
		a[j2] = x1r - x3i;
		a[j2 + 1] = x1i + x3r;
		a[j3] = x1r + x3i;
		a[j3 + 1] = x1i - x3r;
		wn4r = w[1];
		csc1 = w[2];
		csc3 = w[3];
		wd1r = 1;
		wd1i = 0;
		wd3r = 1;
		wd3i = 0;
		k = 0;
		for (j = 2; j < mh - 2; j += 4) {
			k += 4;
			wk1r = csc1 * (wd1r + w[k]);
			wk1i = csc1 * (wd1i + w[k + 1]);
			wk3r = csc3 * (wd3r + w[k + 2]);
			wk3i = csc3 * (wd3i - w[k + 3]);
			wd1r = w[k];
			wd1i = w[k + 1];
			wd3r = w[k + 2];
			wd3i = -w[k + 3];
			j1 = j + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j] + a[j2];
			x0i = a[j + 1] + a[j2 + 1];
			x1r = a[j] - a[j2];
			x1i = a[j + 1] - a[j2 + 1];
			y0r = a[j + 2] + a[j2 + 2];
			y0i = a[j + 3] + a[j2 + 3];
			y1r = a[j + 2] - a[j2 + 2];
			y1i = a[j + 3] - a[j2 + 3];
			x2r = a[j1] + a[j3];
			x2i = a[j1 + 1] + a[j3 + 1];
			x3r = a[j1] - a[j3];
			x3i = a[j1 + 1] - a[j3 + 1];
			y2r = a[j1 + 2] + a[j3 + 2];
			y2i = a[j1 + 3] + a[j3 + 3];
			y3r = a[j1 + 2] - a[j3 + 2];
			y3i = a[j1 + 3] - a[j3 + 3];
			a[j] = x0r + x2r;
			a[j + 1] = x0i + x2i;
			a[j + 2] = y0r + y2r;
			a[j + 3] = y0i + y2i;
			a[j1] = x0r - x2r;
			a[j1 + 1] = x0i - x2i;
			a[j1 + 2] = y0r - y2r;
			a[j1 + 3] = y0i - y2i;
			x0r = x1r - x3i;
			x0i = x1i + x3r;
			a[j2] = wk1r * x0r - wk1i * x0i;
			a[j2 + 1] = wk1r * x0i + wk1i * x0r;
			x0r = y1r - y3i;
			x0i = y1i + y3r;
			a[j2 + 2] = wd1r * x0r - wd1i * x0i;
			a[j2 + 3] = wd1r * x0i + wd1i * x0r;
			x0r = x1r + x3i;
			x0i = x1i - x3r;
			a[j3] = wk3r * x0r + wk3i * x0i;
			a[j3 + 1] = wk3r * x0i - wk3i * x0r;
			x0r = y1r + y3i;
			x0i = y1i - y3r;
			a[j3 + 2] = wd3r * x0r + wd3i * x0i;
			a[j3 + 3] = wd3r * x0i - wd3i * x0r;
			j0 = m - j;
			j1 = j0 + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j0] + a[j2];
			x0i = a[j0 + 1] + a[j2 + 1];
			x1r = a[j0] - a[j2];
			x1i = a[j0 + 1] - a[j2 + 1];
			y0r = a[j0 - 2] + a[j2 - 2];
			y0i = a[j0 - 1] + a[j2 - 1];
			y1r = a[j0 - 2] - a[j2 - 2];
			y1i = a[j0 - 1] - a[j2 - 1];
			x2r = a[j1] + a[j3];
			x2i = a[j1 + 1] + a[j3 + 1];
			x3r = a[j1] - a[j3];
			x3i = a[j1 + 1] - a[j3 + 1];
			y2r = a[j1 - 2] + a[j3 - 2];
			y2i = a[j1 - 1] + a[j3 - 1];
			y3r = a[j1 - 2] - a[j3 - 2];
			y3i = a[j1 - 1] - a[j3 - 1];
			a[j0] = x0r + x2r;
			a[j0 + 1] = x0i + x2i;
			a[j0 - 2] = y0r + y2r;
			a[j0 - 1] = y0i + y2i;
			a[j1] = x0r - x2r;
			a[j1 + 1] = x0i - x2i;
			a[j1 - 2] = y0r - y2r;
			a[j1 - 1] = y0i - y2i;
			x0r = x1r - x3i;
			x0i = x1i + x3r;
			a[j2] = wk1i * x0r - wk1r * x0i;
			a[j2 + 1] = wk1i * x0i + wk1r * x0r;
			x0r = y1r - y3i;
			x0i = y1i + y3r;
			a[j2 - 2] = wd1i * x0r - wd1r * x0i;
			a[j2 - 1] = wd1i * x0i + wd1r * x0r;
			x0r = x1r + x3i;
			x0i = x1i - x3r;
			a[j3] = wk3i * x0r + wk3r * x0i;
			a[j3 + 1] = wk3i * x0i - wk3r * x0r;
			x0r = y1r + y3i;
			x0i = y1i - y3r;
			a[j3 - 2] = wd3i * x0r + wd3r * x0i;
			a[j3 - 1] = wd3i * x0i - wd3r * x0r;
		}
		wk1r = csc1 * (wd1r + wn4r);
		wk1i = csc1 * (wd1i + wn4r);
		wk3r = csc3 * (wd3r - wn4r);
		wk3i = csc3 * (wd3i - wn4r);
		j0 = mh;
		j1 = j0 + m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[j0 - 2] + a[j2 - 2];
		x0i = a[j0 - 1] + a[j2 - 1];
		x1r = a[j0 - 2] - a[j2 - 2];
		x1i = a[j0 - 1] - a[j2 - 1];
		x2r = a[j1 - 2] + a[j3 - 2];
		x2i = a[j1 - 1] + a[j3 - 1];
		x3r = a[j1 - 2] - a[j3 - 2];
		x3i = a[j1 - 1] - a[j3 - 1];
		a[j0 - 2] = x0r + x2r;
		a[j0 - 1] = x0i + x2i;
		a[j1 - 2] = x0r - x2r;
		a[j1 - 1] = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		a[j2 - 2] = wk1r * x0r - wk1i * x0i;
		a[j2 - 1] = wk1r * x0i + wk1i * x0r;
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		a[j3 - 2] = wk3r * x0r + wk3i * x0i;
		a[j3 - 1] = wk3r * x0i - wk3i * x0r;
		x0r = a[j0] + a[j2];
		x0i = a[j0 + 1] + a[j2 + 1];
		x1r = a[j0] - a[j2];
		x1i = a[j0 + 1] - a[j2 + 1];
		x2r = a[j1] + a[j3];
		x2i = a[j1 + 1] + a[j3 + 1];
		x3r = a[j1] - a[j3];
		x3i = a[j1 + 1] - a[j3 + 1];
		a[j0] = x0r + x2r;
		a[j0 + 1] = x0i + x2i;
		a[j1] = x0r - x2r;
		a[j1 + 1] = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		a[j2] = wn4r * (x0r - x0i);
		a[j2 + 1] = wn4r * (x0i + x0r);
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		a[j3] = -wn4r * (x0r + x0i);
		a[j3 + 1] = -wn4r * (x0i - x0r);
		x0r = a[j0 + 2] + a[j2 + 2];
		x0i = a[j0 + 3] + a[j2 + 3];
		x1r = a[j0 + 2] - a[j2 + 2];
		x1i = a[j0 + 3] - a[j2 + 3];
		x2r = a[j1 + 2] + a[j3 + 2];
		x2i = a[j1 + 3] + a[j3 + 3];
		x3r = a[j1 + 2] - a[j3 + 2];
		x3i = a[j1 + 3] - a[j3 + 3];
		a[j0 + 2] = x0r + x2r;
		a[j0 + 3] = x0i + x2i;
		a[j1 + 2] = x0r - x2r;
		a[j1 + 3] = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		a[j2 + 2] = wk1i * x0r - wk1r * x0i;
		a[j2 + 3] = wk1i * x0i + wk1r * x0r;
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		a[j3 + 2] = wk3i * x0r + wk3r * x0i;
		a[j3 + 3] = wk3i * x0i - wk3r * x0r;
	}


	static void cftb1st(int n, REAL *a, REAL *w)
	{
		int j, j0, j1, j2, j3, k, m, mh;
		REAL wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
			wd1r, wd1i, wd3r, wd3i;
		REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
			y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;

		mh = n >> 3;
		m = 2 * mh;
		j1 = m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[0] + a[j2];
		x0i = -a[1] - a[j2 + 1];
		x1r = a[0] - a[j2];
		x1i = -a[1] + a[j2 + 1];
		x2r = a[j1] + a[j3];
		x2i = a[j1 + 1] + a[j3 + 1];
		x3r = a[j1] - a[j3];
		x3i = a[j1 + 1] - a[j3 + 1];
		a[0] = x0r + x2r;
		a[1] = x0i - x2i;
		a[j1] = x0r - x2r;
		a[j1 + 1] = x0i + x2i;
		a[j2] = x1r + x3i;
		a[j2 + 1] = x1i + x3r;
		a[j3] = x1r - x3i;
		a[j3 + 1] = x1i - x3r;
		wn4r = w[1];
		csc1 = w[2];
		csc3 = w[3];
		wd1r = 1;
		wd1i = 0;
		wd3r = 1;
		wd3i = 0;
		k = 0;
		for (j = 2; j < mh - 2; j += 4) {
			k += 4;
			wk1r = csc1 * (wd1r + w[k]);
			wk1i = csc1 * (wd1i + w[k + 1]);
			wk3r = csc3 * (wd3r + w[k + 2]);
			wk3i = csc3 * (wd3i - w[k + 3]);
			wd1r = w[k];
			wd1i = w[k + 1];
			wd3r = w[k + 2];
			wd3i = -w[k + 3];
			j1 = j + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j] + a[j2];
			x0i = -a[j + 1] - a[j2 + 1];
			x1r = a[j] - a[j2];
			x1i = -a[j + 1] + a[j2 + 1];
			y0r = a[j + 2] + a[j2 + 2];
			y0i = -a[j + 3] - a[j2 + 3];
			y1r = a[j + 2] - a[j2 + 2];
			y1i = -a[j + 3] + a[j2 + 3];
			x2r = a[j1] + a[j3];
			x2i = a[j1 + 1] + a[j3 + 1];
			x3r = a[j1] - a[j3];
			x3i = a[j1 + 1] - a[j3 + 1];
			y2r = a[j1 + 2] + a[j3 + 2];
			y2i = a[j1 + 3] + a[j3 + 3];
			y3r = a[j1 + 2] - a[j3 + 2];
			y3i = a[j1 + 3] - a[j3 + 3];
			a[j] = x0r + x2r;
			a[j + 1] = x0i - x2i;
			a[j + 2] = y0r + y2r;
			a[j + 3] = y0i - y2i;
			a[j1] = x0r - x2r;
			a[j1 + 1] = x0i + x2i;
			a[j1 + 2] = y0r - y2r;
			a[j1 + 3] = y0i + y2i;
			x0r = x1r + x3i;
			x0i = x1i + x3r;
			a[j2] = wk1r * x0r - wk1i * x0i;
			a[j2 + 1] = wk1r * x0i + wk1i * x0r;
			x0r = y1r + y3i;
			x0i = y1i + y3r;
			a[j2 + 2] = wd1r * x0r - wd1i * x0i;
			a[j2 + 3] = wd1r * x0i + wd1i * x0r;
			x0r = x1r - x3i;
			x0i = x1i - x3r;
			a[j3] = wk3r * x0r + wk3i * x0i;
			a[j3 + 1] = wk3r * x0i - wk3i * x0r;
			x0r = y1r - y3i;
			x0i = y1i - y3r;
			a[j3 + 2] = wd3r * x0r + wd3i * x0i;
			a[j3 + 3] = wd3r * x0i - wd3i * x0r;
			j0 = m - j;
			j1 = j0 + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j0] + a[j2];
			x0i = -a[j0 + 1] - a[j2 + 1];
			x1r = a[j0] - a[j2];
			x1i = -a[j0 + 1] + a[j2 + 1];
			y0r = a[j0 - 2] + a[j2 - 2];
			y0i = -a[j0 - 1] - a[j2 - 1];
			y1r = a[j0 - 2] - a[j2 - 2];
			y1i = -a[j0 - 1] + a[j2 - 1];
			x2r = a[j1] + a[j3];
			x2i = a[j1 + 1] + a[j3 + 1];
			x3r = a[j1] - a[j3];
			x3i = a[j1 + 1] - a[j3 + 1];
			y2r = a[j1 - 2] + a[j3 - 2];
			y2i = a[j1 - 1] + a[j3 - 1];
			y3r = a[j1 - 2] - a[j3 - 2];
			y3i = a[j1 - 1] - a[j3 - 1];
			a[j0] = x0r + x2r;
			a[j0 + 1] = x0i - x2i;
			a[j0 - 2] = y0r + y2r;
			a[j0 - 1] = y0i - y2i;
			a[j1] = x0r - x2r;
			a[j1 + 1] = x0i + x2i;
			a[j1 - 2] = y0r - y2r;
			a[j1 - 1] = y0i + y2i;
			x0r = x1r + x3i;
			x0i = x1i + x3r;
			a[j2] = wk1i * x0r - wk1r * x0i;
			a[j2 + 1] = wk1i * x0i + wk1r * x0r;
			x0r = y1r + y3i;
			x0i = y1i + y3r;
			a[j2 - 2] = wd1i * x0r - wd1r * x0i;
			a[j2 - 1] = wd1i * x0i + wd1r * x0r;
			x0r = x1r - x3i;
			x0i = x1i - x3r;
			a[j3] = wk3i * x0r + wk3r * x0i;
			a[j3 + 1] = wk3i * x0i - wk3r * x0r;
			x0r = y1r - y3i;
			x0i = y1i - y3r;
			a[j3 - 2] = wd3i * x0r + wd3r * x0i;
			a[j3 - 1] = wd3i * x0i - wd3r * x0r;
		}
		wk1r = csc1 * (wd1r + wn4r);
		wk1i = csc1 * (wd1i + wn4r);
		wk3r = csc3 * (wd3r - wn4r);
		wk3i = csc3 * (wd3i - wn4r);
		j0 = mh;
		j1 = j0 + m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[j0 - 2] + a[j2 - 2];
		x0i = -a[j0 - 1] - a[j2 - 1];
		x1r = a[j0 - 2] - a[j2 - 2];
		x1i = -a[j0 - 1] + a[j2 - 1];
		x2r = a[j1 - 2] + a[j3 - 2];
		x2i = a[j1 - 1] + a[j3 - 1];
		x3r = a[j1 - 2] - a[j3 - 2];
		x3i = a[j1 - 1] - a[j3 - 1];
		a[j0 - 2] = x0r + x2r;
		a[j0 - 1] = x0i - x2i;
		a[j1 - 2] = x0r - x2r;
		a[j1 - 1] = x0i + x2i;
		x0r = x1r + x3i;
		x0i = x1i + x3r;
		a[j2 - 2] = wk1r * x0r - wk1i * x0i;
		a[j2 - 1] = wk1r * x0i + wk1i * x0r;
		x0r = x1r - x3i;
		x0i = x1i - x3r;
		a[j3 - 2] = wk3r * x0r + wk3i * x0i;
		a[j3 - 1] = wk3r * x0i - wk3i * x0r;
		x0r = a[j0] + a[j2];
		x0i = -a[j0 + 1] - a[j2 + 1];
		x1r = a[j0] - a[j2];
		x1i = -a[j0 + 1] + a[j2 + 1];
		x2r = a[j1] + a[j3];
		x2i = a[j1 + 1] + a[j3 + 1];
		x3r = a[j1] - a[j3];
		x3i = a[j1 + 1] - a[j3 + 1];
		a[j0] = x0r + x2r;
		a[j0 + 1] = x0i - x2i;
		a[j1] = x0r - x2r;
		a[j1 + 1] = x0i + x2i;
		x0r = x1r + x3i;
		x0i = x1i + x3r;
		a[j2] = wn4r * (x0r - x0i);
		a[j2 + 1] = wn4r * (x0i + x0r);
		x0r = x1r - x3i;
		x0i = x1i - x3r;
		a[j3] = -wn4r * (x0r + x0i);
		a[j3 + 1] = -wn4r * (x0i - x0r);
		x0r = a[j0 + 2] + a[j2 + 2];
		x0i = -a[j0 + 3] - a[j2 + 3];
		x1r = a[j0 + 2] - a[j2 + 2];
		x1i = -a[j0 + 3] + a[j2 + 3];
		x2r = a[j1 + 2] + a[j3 + 2];
		x2i = a[j1 + 3] + a[j3 + 3];
		x3r = a[j1 + 2] - a[j3 + 2];
		x3i = a[j1 + 3] - a[j3 + 3];
		a[j0 + 2] = x0r + x2r;
		a[j0 + 3] = x0i - x2i;
		a[j1 + 2] = x0r - x2r;
		a[j1 + 3] = x0i + x2i;
		x0r = x1r + x3i;
		x0i = x1i + x3r;
		a[j2 + 2] = wk1i * x0r - wk1r * x0i;
		a[j2 + 3] = wk1i * x0i + wk1r * x0r;
		x0r = x1r - x3i;
		x0i = x1i - x3r;
		a[j3 + 2] = wk3i * x0r + wk3r * x0i;
		a[j3 + 3] = wk3i * x0i - wk3r * x0r;
	}


	static void cftrec1(int n, REAL *a, int nw, REAL *w)
	{
		int m;

		m = n >> 2;
		cftmdl1(n, a, &w[nw - 2 * m]);
		if (n > CDFT_RECURSIVE_N) {
			cftrec1(m, a, nw, w);
			cftrec2(m, &a[m], nw, w);
			cftrec1(m, &a[2 * m], nw, w);
			cftrec1(m, &a[3 * m], nw, w);
		} else {
			cftexp1(n, a, nw, w);
		}
	}


	static void cftrec2(int n, REAL *a, int nw, REAL *w)
	{
		int m;

		m = n >> 2;
		cftmdl2(n, a, &w[nw - n]);
		if (n > CDFT_RECURSIVE_N) {
			cftrec1(m, a, nw, w);
			cftrec2(m, &a[m], nw, w);
			cftrec1(m, &a[2 * m], nw, w);
			cftrec2(m, &a[3 * m], nw, w);
		} else {
			cftexp2(n, a, nw, w);
		}
	}


	static void cftexp1(int n, REAL *a, int nw, REAL *w)
	{
		int j, k, l;

		l = n >> 2;
		while (l > 128) {
			for (k = l; k < n; k <<= 2) {
				for (j = k - l; j < n; j += 4 * k) {
					cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
					cftmdl2(l, &a[k + j], &w[nw - l]);
					cftmdl1(l, &a[2 * k + j], &w[nw - (l >> 1)]);
				}
			}
			cftmdl1(l, &a[n - l], &w[nw - (l >> 1)]);
			l >>= 2;
		}
		for (k = l; k < n; k <<= 2) {
			for (j = k - l; j < n; j += 4 * k) {
				cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
				cftfx41(l, &a[j], nw, w);
				cftmdl2(l, &a[k + j], &w[nw - l]);
				cftfx42(l, &a[k + j], nw, w);
				cftmdl1(l, &a[2 * k + j], &w[nw - (l >> 1)]);
				cftfx41(l, &a[2 * k + j], nw, w);
			}
		}
		cftmdl1(l, &a[n - l], &w[nw - (l >> 1)]);
		cftfx41(l, &a[n - l], nw, w);
	}


	static void cftexp2(int n, REAL *a, int nw, REAL *w)
	{
		int j, k, l, m;

		m = n >> 1;
		l = n >> 2;
		while (l > 128) {
			for (k = l; k < m; k <<= 2) {
				for (j = k - l; j < m; j += 2 * k) {
					cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
					cftmdl1(l, &a[m + j], &w[nw - (l >> 1)]);
				}
				for (j = 2 * k - l; j < m; j += 4 * k) {
					cftmdl2(l, &a[j], &w[nw - l]);
					cftmdl2(l, &a[m + j], &w[nw - l]);
				}
			}
			l >>= 2;
		}
		for (k = l; k < m; k <<= 2) {
			for (j = k - l; j < m; j += 2 * k) {
				cftmdl1(l, &a[j], &w[nw - (l >> 1)]);
				cftfx41(l, &a[j], nw, w);
				cftmdl1(l, &a[m + j], &w[nw - (l >> 1)]);
				cftfx41(l, &a[m + j], nw, w);
			}
			for (j = 2 * k - l; j < m; j += 4 * k) {
				cftmdl2(l, &a[j], &w[nw - l]);
				cftfx42(l, &a[j], nw, w);
				cftmdl2(l, &a[m + j], &w[nw - l]);
				cftfx42(l, &a[m + j], nw, w);
			}
		}
	}


	static void cftmdl1(int n, REAL *a, REAL *w)
	{
		int j, j0, j1, j2, j3, k, m, mh;
		REAL wn4r, wk1r, wk1i, wk3r, wk3i;
		REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

		mh = n >> 3;
		m = 2 * mh;
		j1 = m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[0] + a[j2];
		x0i = a[1] + a[j2 + 1];
		x1r = a[0] - a[j2];
		x1i = a[1] - a[j2 + 1];
		x2r = a[j1] + a[j3];
		x2i = a[j1 + 1] + a[j3 + 1];
		x3r = a[j1] - a[j3];
		x3i = a[j1 + 1] - a[j3 + 1];
		a[0] = x0r + x2r;
		a[1] = x0i + x2i;
		a[j1] = x0r - x2r;
		a[j1 + 1] = x0i - x2i;
		a[j2] = x1r - x3i;
		a[j2 + 1] = x1i + x3r;
		a[j3] = x1r + x3i;
		a[j3 + 1] = x1i - x3r;
		wn4r = w[1];
		k = 0;
		for (j = 2; j < mh; j += 2) {
			k += 4;
			wk1r = w[k];
			wk1i = w[k + 1];
			wk3r = w[k + 2];
			wk3i = -w[k + 3];
			j1 = j + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j] + a[j2];
			x0i = a[j + 1] + a[j2 + 1];
			x1r = a[j] - a[j2];
			x1i = a[j + 1] - a[j2 + 1];
			x2r = a[j1] + a[j3];
			x2i = a[j1 + 1] + a[j3 + 1];
			x3r = a[j1] - a[j3];
			x3i = a[j1 + 1] - a[j3 + 1];
			a[j] = x0r + x2r;
			a[j + 1] = x0i + x2i;
			a[j1] = x0r - x2r;
			a[j1 + 1] = x0i - x2i;
			x0r = x1r - x3i;
			x0i = x1i + x3r;
			a[j2] = wk1r * x0r - wk1i * x0i;
			a[j2 + 1] = wk1r * x0i + wk1i * x0r;
			x0r = x1r + x3i;
			x0i = x1i - x3r;
			a[j3] = wk3r * x0r + wk3i * x0i;
			a[j3 + 1] = wk3r * x0i - wk3i * x0r;
			j0 = m - j;
			j1 = j0 + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j0] + a[j2];
			x0i = a[j0 + 1] + a[j2 + 1];
			x1r = a[j0] - a[j2];
			x1i = a[j0 + 1] - a[j2 + 1];
			x2r = a[j1] + a[j3];
			x2i = a[j1 + 1] + a[j3 + 1];
			x3r = a[j1] - a[j3];
			x3i = a[j1 + 1] - a[j3 + 1];
			a[j0] = x0r + x2r;
			a[j0 + 1] = x0i + x2i;
			a[j1] = x0r - x2r;
			a[j1 + 1] = x0i - x2i;
			x0r = x1r - x3i;
			x0i = x1i + x3r;
			a[j2] = wk1i * x0r - wk1r * x0i;
			a[j2 + 1] = wk1i * x0i + wk1r * x0r;
			x0r = x1r + x3i;
			x0i = x1i - x3r;
			a[j3] = wk3i * x0r + wk3r * x0i;
			a[j3 + 1] = wk3i * x0i - wk3r * x0r;
		}
		j0 = mh;
		j1 = j0 + m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[j0] + a[j2];
		x0i = a[j0 + 1] + a[j2 + 1];
		x1r = a[j0] - a[j2];
		x1i = a[j0 + 1] - a[j2 + 1];
		x2r = a[j1] + a[j3];
		x2i = a[j1 + 1] + a[j3 + 1];
		x3r = a[j1] - a[j3];
		x3i = a[j1 + 1] - a[j3 + 1];
		a[j0] = x0r + x2r;
		a[j0 + 1] = x0i + x2i;
		a[j1] = x0r - x2r;
		a[j1 + 1] = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		a[j2] = wn4r * (x0r - x0i);
		a[j2 + 1] = wn4r * (x0i + x0r);
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		a[j3] = -wn4r * (x0r + x0i);
		a[j3 + 1] = -wn4r * (x0i - x0r);
	}


	static void cftmdl2(int n, REAL *a, REAL *w)
	{
		int j, j0, j1, j2, j3, k, kr, m, mh;
		REAL wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
		REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;

		mh = n >> 3;
		m = 2 * mh;
		wn4r = w[1];
		j1 = m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[0] - a[j2 + 1];
		x0i = a[1] + a[j2];
		x1r = a[0] + a[j2 + 1];
		x1i = a[1] - a[j2];
		x2r = a[j1] - a[j3 + 1];
		x2i = a[j1 + 1] + a[j3];
		x3r = a[j1] + a[j3 + 1];
		x3i = a[j1 + 1] - a[j3];
		y0r = wn4r * (x2r - x2i);
		y0i = wn4r * (x2i + x2r);
		a[0] = x0r + y0r;
		a[1] = x0i + y0i;
		a[j1] = x0r - y0r;
		a[j1 + 1] = x0i - y0i;
		y0r = wn4r * (x3r - x3i);
		y0i = wn4r * (x3i + x3r);
		a[j2] = x1r - y0i;
		a[j2 + 1] = x1i + y0r;
		a[j3] = x1r + y0i;
		a[j3 + 1] = x1i - y0r;
		k = 0;
		kr = 2 * m;
		for (j = 2; j < mh; j += 2) {
			k += 4;
			wk1r = w[k];
			wk1i = w[k + 1];
			wk3r = w[k + 2];
			wk3i = -w[k + 3];
			kr -= 4;
			wd1i = w[kr];
			wd1r = w[kr + 1];
			wd3i = w[kr + 2];
			wd3r = -w[kr + 3];
			j1 = j + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j] - a[j2 + 1];
			x0i = a[j + 1] + a[j2];
			x1r = a[j] + a[j2 + 1];
			x1i = a[j + 1] - a[j2];
			x2r = a[j1] - a[j3 + 1];
			x2i = a[j1 + 1] + a[j3];
			x3r = a[j1] + a[j3 + 1];
			x3i = a[j1 + 1] - a[j3];
			y0r = wk1r * x0r - wk1i * x0i;
			y0i = wk1r * x0i + wk1i * x0r;
			y2r = wd1r * x2r - wd1i * x2i;
			y2i = wd1r * x2i + wd1i * x2r;
			a[j] = y0r + y2r;
			a[j + 1] = y0i + y2i;
			a[j1] = y0r - y2r;
			a[j1 + 1] = y0i - y2i;
			y0r = wk3r * x1r + wk3i * x1i;
			y0i = wk3r * x1i - wk3i * x1r;
			y2r = wd3r * x3r + wd3i * x3i;
			y2i = wd3r * x3i - wd3i * x3r;
			a[j2] = y0r + y2r;
			a[j2 + 1] = y0i + y2i;
			a[j3] = y0r - y2r;
			a[j3 + 1] = y0i - y2i;
			j0 = m - j;
			j1 = j0 + m;
			j2 = j1 + m;
			j3 = j2 + m;
			x0r = a[j0] - a[j2 + 1];
			x0i = a[j0 + 1] + a[j2];
			x1r = a[j0] + a[j2 + 1];
			x1i = a[j0 + 1] - a[j2];
			x2r = a[j1] - a[j3 + 1];
			x2i = a[j1 + 1] + a[j3];
			x3r = a[j1] + a[j3 + 1];
			x3i = a[j1 + 1] - a[j3];
			y0r = wd1i * x0r - wd1r * x0i;
			y0i = wd1i * x0i + wd1r * x0r;
			y2r = wk1i * x2r - wk1r * x2i;
			y2i = wk1i * x2i + wk1r * x2r;
			a[j0] = y0r + y2r;
			a[j0 + 1] = y0i + y2i;
			a[j1] = y0r - y2r;
			a[j1 + 1] = y0i - y2i;
			y0r = wd3i * x1r + wd3r * x1i;
			y0i = wd3i * x1i - wd3r * x1r;
			y2r = wk3i * x3r + wk3r * x3i;
			y2i = wk3i * x3i - wk3r * x3r;
			a[j2] = y0r + y2r;
			a[j2 + 1] = y0i + y2i;
			a[j3] = y0r - y2r;
			a[j3 + 1] = y0i - y2i;
		}
		wk1r = w[m];
		wk1i = w[m + 1];
		j0 = mh;
		j1 = j0 + m;
		j2 = j1 + m;
		j3 = j2 + m;
		x0r = a[j0] - a[j2 + 1];
		x0i = a[j0 + 1] + a[j2];
		x1r = a[j0] + a[j2 + 1];
		x1i = a[j0 + 1] - a[j2];
		x2r = a[j1] - a[j3 + 1];
		x2i = a[j1 + 1] + a[j3];
		x3r = a[j1] + a[j3 + 1];
		x3i = a[j1 + 1] - a[j3];
		y0r = wk1r * x0r - wk1i * x0i;
		y0i = wk1r * x0i + wk1i * x0r;
		y2r = wk1i * x2r - wk1r * x2i;
		y2i = wk1i * x2i + wk1r * x2r;
		a[j0] = y0r + y2r;
		a[j0 + 1] = y0i + y2i;
		a[j1] = y0r - y2r;
		a[j1 + 1] = y0i - y2i;
		y0r = wk1i * x1r - wk1r * x1i;
		y0i = wk1i * x1i + wk1r * x1r;
		y2r = wk1r * x3r - wk1i * x3i;
		y2i = wk1r * x3i + wk1i * x3r;
		a[j2] = y0r - y2r;
		a[j2 + 1] = y0i - y2i;
		a[j3] = y0r + y2r;
		a[j3 + 1] = y0i + y2i;
	}


	static void cftfx41(int n, REAL *a, int nw, REAL *w)
	{
		if (n == 128) {
			cftf161(a, &w[nw - 8]);
			cftf162(&a[32], &w[nw - 32]);
			cftf161(&a[64], &w[nw - 8]);
			cftf161(&a[96], &w[nw - 8]);
		} else {
			cftf081(a, &w[nw - 16]);
			cftf082(&a[16], &w[nw - 16]);
			cftf081(&a[32], &w[nw - 16]);
			cftf081(&a[48], &w[nw - 16]);
		}
	}


	static void cftfx42(int n, REAL *a, int nw, REAL *w)
	{
		if (n == 128) {
			cftf161(a, &w[nw - 8]);
			cftf162(&a[32], &w[nw - 32]);
			cftf161(&a[64], &w[nw - 8]);
			cftf162(&a[96], &w[nw - 32]);
		} else {
			cftf081(a, &w[nw - 16]);
			cftf082(&a[16], &w[nw - 16]);
			cftf081(&a[32], &w[nw - 16]);
			cftf082(&a[48], &w[nw - 16]);
		}
	}


	static void cftf161(REAL *a, REAL *w)
	{
		REAL wn4r, wk1r, wk1i,
			x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
			y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
			y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
			y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
			y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;

		wn4r = w[1];
		wk1i = wn4r * w[2];
		wk1r = wk1i + w[2];
		x0r = a[0] + a[16];
		x0i = a[1] + a[17];
		x1r = a[0] - a[16];
		x1i = a[1] - a[17];
		x2r = a[8] + a[24];
		x2i = a[9] + a[25];
		x3r = a[8] - a[24];
		x3i = a[9] - a[25];
		y0r = x0r + x2r;
		y0i = x0i + x2i;
		y4r = x0r - x2r;
		y4i = x0i - x2i;
		y8r = x1r - x3i;
		y8i = x1i + x3r;
		y12r = x1r + x3i;
		y12i = x1i - x3r;
		x0r = a[2] + a[18];
		x0i = a[3] + a[19];
		x1r = a[2] - a[18];
		x1i = a[3] - a[19];
		x2r = a[10] + a[26];
		x2i = a[11] + a[27];
		x3r = a[10] - a[26];
		x3i = a[11] - a[27];
		y1r = x0r + x2r;
		y1i = x0i + x2i;
		y5r = x0r - x2r;
		y5i = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		y9r = wk1r * x0r - wk1i * x0i;
		y9i = wk1r * x0i + wk1i * x0r;
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		y13r = wk1i * x0r - wk1r * x0i;
		y13i = wk1i * x0i + wk1r * x0r;
		x0r = a[4] + a[20];
		x0i = a[5] + a[21];
		x1r = a[4] - a[20];
		x1i = a[5] - a[21];
		x2r = a[12] + a[28];
		x2i = a[13] + a[29];
		x3r = a[12] - a[28];
		x3i = a[13] - a[29];
		y2r = x0r + x2r;
		y2i = x0i + x2i;
		y6r = x0r - x2r;
		y6i = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		y10r = wn4r * (x0r - x0i);
		y10i = wn4r * (x0i + x0r);
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		y14r = wn4r * (x0r + x0i);
		y14i = wn4r * (x0i - x0r);
		x0r = a[6] + a[22];
		x0i = a[7] + a[23];
		x1r = a[6] - a[22];
		x1i = a[7] - a[23];
		x2r = a[14] + a[30];
		x2i = a[15] + a[31];
		x3r = a[14] - a[30];
		x3i = a[15] - a[31];
		y3r = x0r + x2r;
		y3i = x0i + x2i;
		y7r = x0r - x2r;
		y7i = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		y11r = wk1i * x0r - wk1r * x0i;
		y11i = wk1i * x0i + wk1r * x0r;
		x0r = x1r + x3i;
		x0i = x1i - x3r;
		y15r = wk1r * x0r - wk1i * x0i;
		y15i = wk1r * x0i + wk1i * x0r;
		x0r = y12r - y14r;
		x0i = y12i - y14i;
		x1r = y12r + y14r;
		x1i = y12i + y14i;
		x2r = y13r - y15r;
		x2i = y13i - y15i;
		x3r = y13r + y15r;
		x3i = y13i + y15i;
		a[24] = x0r + x2r;
		a[25] = x0i + x2i;
		a[26] = x0r - x2r;
		a[27] = x0i - x2i;
		a[28] = x1r - x3i;
		a[29] = x1i + x3r;
		a[30] = x1r + x3i;
		a[31] = x1i - x3r;
		x0r = y8r + y10r;
		x0i = y8i + y10i;
		x1r = y8r - y10r;
		x1i = y8i - y10i;
		x2r = y9r + y11r;
		x2i = y9i + y11i;
		x3r = y9r - y11r;
		x3i = y9i - y11i;
		a[16] = x0r + x2r;
		a[17] = x0i + x2i;
		a[18] = x0r - x2r;
		a[19] = x0i - x2i;
		a[20] = x1r - x3i;
		a[21] = x1i + x3r;
		a[22] = x1r + x3i;
		a[23] = x1i - x3r;
		x0r = y5r - y7i;
		x0i = y5i + y7r;
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		x0r = y5r + y7i;
		x0i = y5i - y7r;
		x3r = wn4r * (x0r - x0i);
		x3i = wn4r * (x0i + x0r);
		x0r = y4r - y6i;
		x0i = y4i + y6r;
		x1r = y4r + y6i;
		x1i = y4i - y6r;
		a[8] = x0r + x2r;
		a[9] = x0i + x2i;
		a[10] = x0r - x2r;
		a[11] = x0i - x2i;
		a[12] = x1r - x3i;
		a[13] = x1i + x3r;
		a[14] = x1r + x3i;
		a[15] = x1i - x3r;
		x0r = y0r + y2r;
		x0i = y0i + y2i;
		x1r = y0r - y2r;
		x1i = y0i - y2i;
		x2r = y1r + y3r;
		x2i = y1i + y3i;
		x3r = y1r - y3r;
		x3i = y1i - y3i;
		a[0] = x0r + x2r;
		a[1] = x0i + x2i;
		a[2] = x0r - x2r;
		a[3] = x0i - x2i;
		a[4] = x1r - x3i;
		a[5] = x1i + x3r;
		a[6] = x1r + x3i;
		a[7] = x1i - x3r;
	}


	static void cftf162(REAL *a, REAL *w)
	{
		REAL wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
			x0r, x0i, x1r, x1i, x2r, x2i,
			y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
			y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
			y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
			y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;

		wn4r = w[1];
		wk1r = w[4];
		wk1i = w[5];
		wk3r = w[6];
		wk3i = w[7];
		wk2r = w[8];
		wk2i = w[9];
		x1r = a[0] - a[17];
		x1i = a[1] + a[16];
		x0r = a[8] - a[25];
		x0i = a[9] + a[24];
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		y0r = x1r + x2r;
		y0i = x1i + x2i;
		y4r = x1r - x2r;
		y4i = x1i - x2i;
		x1r = a[0] + a[17];
		x1i = a[1] - a[16];
		x0r = a[8] + a[25];
		x0i = a[9] - a[24];
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		y8r = x1r - x2i;
		y8i = x1i + x2r;
		y12r = x1r + x2i;
		y12i = x1i - x2r;
		x0r = a[2] - a[19];
		x0i = a[3] + a[18];
		x1r = wk1r * x0r - wk1i * x0i;
		x1i = wk1r * x0i + wk1i * x0r;
		x0r = a[10] - a[27];
		x0i = a[11] + a[26];
		x2r = wk3i * x0r - wk3r * x0i;
		x2i = wk3i * x0i + wk3r * x0r;
		y1r = x1r + x2r;
		y1i = x1i + x2i;
		y5r = x1r - x2r;
		y5i = x1i - x2i;
		x0r = a[2] + a[19];
		x0i = a[3] - a[18];
		x1r = wk3r * x0r - wk3i * x0i;
		x1i = wk3r * x0i + wk3i * x0r;
		x0r = a[10] + a[27];
		x0i = a[11] - a[26];
		x2r = wk1r * x0r + wk1i * x0i;
		x2i = wk1r * x0i - wk1i * x0r;
		y9r = x1r - x2r;
		y9i = x1i - x2i;
		y13r = x1r + x2r;
		y13i = x1i + x2i;
		x0r = a[4] - a[21];
		x0i = a[5] + a[20];
		x1r = wk2r * x0r - wk2i * x0i;
		x1i = wk2r * x0i + wk2i * x0r;
		x0r = a[12] - a[29];
		x0i = a[13] + a[28];
		x2r = wk2i * x0r - wk2r * x0i;
		x2i = wk2i * x0i + wk2r * x0r;
		y2r = x1r + x2r;
		y2i = x1i + x2i;
		y6r = x1r - x2r;
		y6i = x1i - x2i;
		x0r = a[4] + a[21];
		x0i = a[5] - a[20];
		x1r = wk2i * x0r - wk2r * x0i;
		x1i = wk2i * x0i + wk2r * x0r;
		x0r = a[12] + a[29];
		x0i = a[13] - a[28];
		x2r = wk2r * x0r - wk2i * x0i;
		x2i = wk2r * x0i + wk2i * x0r;
		y10r = x1r - x2r;
		y10i = x1i - x2i;
		y14r = x1r + x2r;
		y14i = x1i + x2i;
		x0r = a[6] - a[23];
		x0i = a[7] + a[22];
		x1r = wk3r * x0r - wk3i * x0i;
		x1i = wk3r * x0i + wk3i * x0r;
		x0r = a[14] - a[31];
		x0i = a[15] + a[30];
		x2r = wk1i * x0r - wk1r * x0i;
		x2i = wk1i * x0i + wk1r * x0r;
		y3r = x1r + x2r;
		y3i = x1i + x2i;
		y7r = x1r - x2r;
		y7i = x1i - x2i;
		x0r = a[6] + a[23];
		x0i = a[7] - a[22];
		x1r = wk1i * x0r + wk1r * x0i;
		x1i = wk1i * x0i - wk1r * x0r;
		x0r = a[14] + a[31];
		x0i = a[15] - a[30];
		x2r = wk3i * x0r - wk3r * x0i;
		x2i = wk3i * x0i + wk3r * x0r;
		y11r = x1r + x2r;
		y11i = x1i + x2i;
		y15r = x1r - x2r;
		y15i = x1i - x2i;
		x1r = y0r + y2r;
		x1i = y0i + y2i;
		x2r = y1r + y3r;
		x2i = y1i + y3i;
		a[0] = x1r + x2r;
		a[1] = x1i + x2i;
		a[2] = x1r - x2r;
		a[3] = x1i - x2i;
		x1r = y0r - y2r;
		x1i = y0i - y2i;
		x2r = y1r - y3r;
		x2i = y1i - y3i;
		a[4] = x1r - x2i;
		a[5] = x1i + x2r;
		a[6] = x1r + x2i;
		a[7] = x1i - x2r;
		x1r = y4r - y6i;
		x1i = y4i + y6r;
		x0r = y5r - y7i;
		x0i = y5i + y7r;
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		a[8] = x1r + x2r;
		a[9] = x1i + x2i;
		a[10] = x1r - x2r;
		a[11] = x1i - x2i;
		x1r = y4r + y6i;
		x1i = y4i - y6r;
		x0r = y5r + y7i;
		x0i = y5i - y7r;
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		a[12] = x1r - x2i;
		a[13] = x1i + x2r;
		a[14] = x1r + x2i;
		a[15] = x1i - x2r;
		x1r = y8r + y10r;
		x1i = y8i + y10i;
		x2r = y9r - y11r;
		x2i = y9i - y11i;
		a[16] = x1r + x2r;
		a[17] = x1i + x2i;
		a[18] = x1r - x2r;
		a[19] = x1i - x2i;
		x1r = y8r - y10r;
		x1i = y8i - y10i;
		x2r = y9r + y11r;
		x2i = y9i + y11i;
		a[20] = x1r - x2i;
		a[21] = x1i + x2r;
		a[22] = x1r + x2i;
		a[23] = x1i - x2r;
		x1r = y12r - y14i;
		x1i = y12i + y14r;
		x0r = y13r + y15i;
		x0i = y13i - y15r;
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		a[24] = x1r + x2r;
		a[25] = x1i + x2i;
		a[26] = x1r - x2r;
		a[27] = x1i - x2i;
		x1r = y12r + y14i;
		x1i = y12i - y14r;
		x0r = y13r - y15i;
		x0i = y13i + y15r;
		x2r = wn4r * (x0r - x0i);
		x2i = wn4r * (x0i + x0r);
		a[28] = x1r - x2i;
		a[29] = x1i + x2r;
		a[30] = x1r + x2i;
		a[31] = x1i - x2r;
	}


	static void cftf081(REAL *a, REAL *w)
	{
		REAL wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
			y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
			y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

		wn4r = w[1];
		x0r = a[0] + a[8];
		x0i = a[1] + a[9];
		x1r = a[0] - a[8];
		x1i = a[1] - a[9];
		x2r = a[4] + a[12];
		x2i = a[5] + a[13];
		x3r = a[4] - a[12];
		x3i = a[5] - a[13];
		y0r = x0r + x2r;
		y0i = x0i + x2i;
		y2r = x0r - x2r;
		y2i = x0i - x2i;
		y1r = x1r - x3i;
		y1i = x1i + x3r;
		y3r = x1r + x3i;
		y3i = x1i - x3r;
		x0r = a[2] + a[10];
		x0i = a[3] + a[11];
		x1r = a[2] - a[10];
		x1i = a[3] - a[11];
		x2r = a[6] + a[14];
		x2i = a[7] + a[15];
		x3r = a[6] - a[14];
		x3i = a[7] - a[15];
		y4r = x0r + x2r;
		y4i = x0i + x2i;
		y6r = x0r - x2r;
		y6i = x0i - x2i;
		x0r = x1r - x3i;
		x0i = x1i + x3r;
		x2r = x1r + x3i;
		x2i = x1i - x3r;
		y5r = wn4r * (x0r - x0i);
		y5i = wn4r * (x0r + x0i);
		y7r = wn4r * (x2r - x2i);
		y7i = wn4r * (x2r + x2i);
		a[8] = y1r + y5r;
		a[9] = y1i + y5i;
		a[10] = y1r - y5r;
		a[11] = y1i - y5i;
		a[12] = y3r - y7i;
		a[13] = y3i + y7r;
		a[14] = y3r + y7i;
		a[15] = y3i - y7r;
		a[0] = y0r + y4r;
		a[1] = y0i + y4i;
		a[2] = y0r - y4r;
		a[3] = y0i - y4i;
		a[4] = y2r - y6i;
		a[5] = y2i + y6r;
		a[6] = y2r + y6i;
		a[7] = y2i - y6r;
	}


	static void cftf082(REAL *a, REAL *w)
	{
		REAL wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i,
			y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
			y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;

		wn4r = w[1];
		wk1r = w[4];
		wk1i = w[5];
		y0r = a[0] - a[9];
		y0i = a[1] + a[8];
		y1r = a[0] + a[9];
		y1i = a[1] - a[8];
		x0r = a[4] - a[13];
		x0i = a[5] + a[12];
		y2r = wn4r * (x0r - x0i);
		y2i = wn4r * (x0i + x0r);
		x0r = a[4] + a[13];
		x0i = a[5] - a[12];
		y3r = wn4r * (x0r - x0i);
		y3i = wn4r * (x0i + x0r);
		x0r = a[2] - a[11];
		x0i = a[3] + a[10];
		y4r = wk1r * x0r - wk1i * x0i;
		y4i = wk1r * x0i + wk1i * x0r;
		x0r = a[2] + a[11];
		x0i = a[3] - a[10];
		y5r = wk1i * x0r - wk1r * x0i;
		y5i = wk1i * x0i + wk1r * x0r;
		x0r = a[6] - a[15];
		x0i = a[7] + a[14];
		y6r = wk1i * x0r - wk1r * x0i;
		y6i = wk1i * x0i + wk1r * x0r;
		x0r = a[6] + a[15];
		x0i = a[7] - a[14];
		y7r = wk1r * x0r - wk1i * x0i;
		y7i = wk1r * x0i + wk1i * x0r;
		x0r = y0r + y2r;
		x0i = y0i + y2i;
		x1r = y4r + y6r;
		x1i = y4i + y6i;
		a[0] = x0r + x1r;
		a[1] = x0i + x1i;
		a[2] = x0r - x1r;
		a[3] = x0i - x1i;
		x0r = y0r - y2r;
		x0i = y0i - y2i;
		x1r = y4r - y6r;
		x1i = y4i - y6i;
		a[4] = x0r - x1i;
		a[5] = x0i + x1r;
		a[6] = x0r + x1i;
		a[7] = x0i - x1r;
		x0r = y1r - y3i;
		x0i = y1i + y3r;
		x1r = y5r - y7r;
		x1i = y5i - y7i;
		a[8] = x0r + x1r;
		a[9] = x0i + x1i;
		a[10] = x0r - x1r;
		a[11] = x0i - x1i;
		x0r = y1r + y3i;
		x0i = y1i - y3r;
		x1r = y5r + y7r;
		x1i = y5i + y7i;
		a[12] = x0r - x1i;
		a[13] = x0i + x1r;
		a[14] = x0r + x1i;
		a[15] = x0i - x1r;
	}


	static void cftf040(REAL *a)
	{
		REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

		x0r = a[0] + a[4];
		x0i = a[1] + a[5];
		x1r = a[0] - a[4];
		x1i = a[1] - a[5];
		x2r = a[2] + a[6];
		x2i = a[3] + a[7];
		x3r = a[2] - a[6];
		x3i = a[3] - a[7];
		a[0] = x0r + x2r;
		a[1] = x0i + x2i;
		a[4] = x0r - x2r;
		a[5] = x0i - x2i;
		a[2] = x1r - x3i;
		a[3] = x1i + x3r;
		a[6] = x1r + x3i;
		a[7] = x1i - x3r;
	}


	static void cftb040(REAL *a)
	{
		REAL x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;

		x0r = a[0] + a[4];
		x0i = a[1] + a[5];
		x1r = a[0] - a[4];
		x1i = a[1] - a[5];
		x2r = a[2] + a[6];
		x2i = a[3] + a[7];
		x3r = a[2] - a[6];
		x3i = a[3] - a[7];
		a[0] = x0r + x2r;
		a[1] = x0i + x2i;
		a[4] = x0r - x2r;
		a[5] = x0i - x2i;
		a[2] = x1r + x3i;
		a[3] = x1i - x3r;
		a[6] = x1r - x3i;
		a[7] = x1i + x3r;
	}


	static void cftx020(REAL *a)
	{
		REAL x0r, x0i;

		x0r = a[0] - a[2];
		x0i = a[1] - a[3];
		a[0] += a[2];
		a[1] += a[3];
		a[2] = x0r;
		a[3] = x0i;
	}


	static void rftfsub(int n, REAL *a, int nc, REAL *c)
	{
		int j, k, kk, ks, m;
		REAL wkr, wki, xr, xi, yr, yi;

		m = n >> 1;
		ks = 2 * nc / m;
		kk = 0;
		for (j = 2; j < m; j += 2) {
			k = n - j;
			kk += ks;
			wkr = 0.5 - c[nc - kk];
			wki = c[kk];
			xr = a[j] - a[k];
			xi = a[j + 1] + a[k + 1];
			yr = wkr * xr - wki * xi;
			yi = wkr * xi + wki * xr;
			a[j] -= yr;
			a[j + 1] -= yi;
			a[k] += yr;
			a[k + 1] -= yi;
		}
	}


	static void rftbsub(int n, REAL *a, int nc, REAL *c)
	{
		int j, k, kk, ks, m;
		REAL wkr, wki, xr, xi, yr, yi;

		m = n >> 1;
		ks = 2 * nc / m;
		kk = 0;
		for (j = 2; j < m; j += 2) {
			k = n - j;
			kk += ks;
			wkr = 0.5 - c[nc - kk];
			wki = c[kk];
			xr = a[j] - a[k];
			xi = a[j + 1] + a[k + 1];
			yr = wkr * xr + wki * xi;
			yi = wkr * xi - wki * xr;
			a[j] -= yr;
			a[j + 1] -= yi;
			a[k] += yr;
			a[k + 1] -= yi;
		}
	}


	static void dctsub(int n, REAL *a, int nc, REAL *c)
	{
		int j, k, kk, ks, m;
		REAL wkr, wki, xr;

		m = n >> 1;
		ks = nc / n;
		kk = 0;
		for (j = 1; j < m; j++) {
			k = n - j;
			kk += ks;
			wkr = c[kk] - c[nc - kk];
			wki = c[kk] + c[nc - kk];
			xr = wki * a[j] - wkr * a[k];
			a[j] = wkr * a[j] + wki * a[k];
			a[k] = xr;
		}
		a[m] *= c[0];
	}

	static void dstsub(int n, REAL *a, int nc, REAL *c)
	{
		int j, k, kk, ks, m;
		REAL wkr, wki, xr;

		m = n >> 1;
		ks = nc / n;
		kk = 0;
		for (j = 1; j < m; j++) {
			k = n - j;
			kk += ks;
			wkr = c[kk] - c[nc - kk];
			wki = c[kk] + c[nc - kk];
			xr = wki * a[k] - wkr * a[j];
			a[k] = wkr * a[k] + wki * a[j];
			a[j] = xr;
		}
		a[m] *= c[0];
	}
};

#endif //_DSP_MATH_SHARED_H_